Annie Millet, Marta Sanz-Solé
Published 2004-12-09Version 1
Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$ given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric rough paths, extending classical results on Gaussian processes. As a by-product, geometric rough paths associated to elements of the reproducing kernel Hilbert space of the fractional Brownian motion are obtained and an explicit integral representation is given.
A large deviation principle in Hölder norm for multiple fractional integrals
Approximation of rough paths of fractional Brownian motion
On the connection between Molchan-Golosov and Mandelbrot-Van Ness representations of fractional Brownian motion
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